Answered: What stats test should be used to solve…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 26PFA

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What stats test should be used to solve the following?

A positive psychologist compares whether levels of gratitude in a random sample of n = 50 students at her college (M = 40) differ from the mean of college students across the US (μ = 45).

A sports psychologist tested the reaction time of 320 college athletes. She found their average reaction time in a controlled task to be .77 seconds (s = 21). She wondered if the college athletes had faster reactions times than college students on average, who typically reacted in 1.23 seconds.

A school psychologist obtained a sample of 120 fourth-grade kids who engaged in remote learning only during the COVID-19 pandemic. She found their average anxiety score to be M = 168. He compared that mean to the average anxiety score of fourth-grade children before the pandemic, which was μ = 144, with a ?=12σ=12. Did the sample of kids engaged in remote learning have a significantly different level of anxiety?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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